Highest Common Factor of 416, 210, 353 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 416, 210, 353 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 416, 210, 353 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 416, 210, 353 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 416, 210, 353 is 1.
HCF(416, 210, 353) = 1
HCF of 416, 210, 353 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 416, 210, 353 is 1.
Highest Common Factor of 416,210,353 is 1
Step 1: Since 416 > 210, we apply the division lemma to 416 and 210, to get
416 = 210 x 1 + 206
Step 2: Since the reminder 210 ≠ 0, we apply division lemma to 206 and 210, to get
210 = 206 x 1 + 4
Step 3: We consider the new divisor 206 and the new remainder 4, and apply the division lemma to get
206 = 4 x 51 + 2
We consider the new divisor 4 and the new remainder 2, and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 416 and 210 is 2
Notice that 2 = HCF(4,2) = HCF(206,4) = HCF(210,206) = HCF(416,210) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 353 > 2, we apply the division lemma to 353 and 2, to get
353 = 2 x 176 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 353 is 1
Notice that 1 = HCF(2,1) = HCF(353,2) .
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Frequently Asked Questions on HCF of 416, 210, 353 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 416, 210, 353?
Answer: HCF of 416, 210, 353 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 416, 210, 353 using Euclid's Algorithm?
Answer: For arbitrary numbers 416, 210, 353 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.